Question: Compute (iint_{mathcal{S}} mathbf{F} cdot d mathbf{S}) for the given oriented surface. (mathbf{F}=leftlangle e^{z}, z, xightangle, quad Phi(r, s)=(r s, r+s, r)), (0 leq r leq

Compute $\iint_{\mathcal{S}} \mathbf{F} \cdot d \mathbf{S}$ for the given oriented surface.

$\mathbf{F}=\left\langle e^{z}, z, xightangle, \quad \Phi(r, s)=(r s, r+s, r)$, $0 \leq r \leq 1,0 \leq s \leq 1, \quad$ oriented by $\mathbf{T}_{r} \times \mathbf{T}_{s}$

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